x<-c gt

MATRIISIt JA VEKTORIT

> x<-c(1,2,3,4,5)

>

> x

[1] 1 2 3 4 5

>

> x<-1:5

>

> x<-array(1:5,dim=c(5))

> x

[1] 1 2 3 4 5

> x<-array(c(1,2,3),dim=c(5))

> x

[1] 1 2 3 1 2

>

> x<-array(1:20,dim=c(4,5))

> x

[,1] [,2] [,3] [,4] [,5]

[1,] 1 5 9 13 17 [2,] 2 6 10 14 18 [3,] 3 7 11 15 19 [4,] 4 8 12 16 20

> x<-matrix(1:20,nr=4,nc=5)

> x[,1]

[1] 1 2 3 4

> x[3,]

[1] 3 7 11 15 19

>

> x[,c(1,2)]

[,1] [,2]

[1,] 1 5 [2,] 2 6 [3,] 3 7 [4,] 4 8

>

> i<-array(c(1:3,3:1),dim=c(3,2))

> i

[,1] [,2]

[1,] 1 3 [2,] 2 2 [3,] 3 1

> x[i]

[1] 9 6 3

> x[i]<-0

> x

[,1] [,2] [,3] [,4] [,5]

[1,] 1 5 0 13 17 [2,] 2 0 10 14 18 [3,] 0 7 11 15 19 [4,] 4 8 12 16 20

>

> m1<-matrix(data=1,nr=2,nc=2)

> m1

[,1] [,2]

[1,] 1 1 [2,] 1 1

> m2<-matrix(data=2,nr=2,nc=2)

> m2

[,1] [,2]

[1,] 2 2 [2,] 2 2

> rbind(m1,m2) [,1] [,2]

[1,] 1 1 [2,] 1 1 [3,] 2 2 [4,] 2 2

> cbind(m1,m2) [,1] [,2] [,3] [,4]

[1,] 1 1 2 2

[2,] 1 1 2 2

>

> tulo<-rbind(m1,m2) %*% cbind(m1,m2)

> tulo

[,1] [,2] [,3] [,4]

[1,] 2 2 4 4 [2,] 2 2 4 4 [3,] 4 4 8 8 [4,] 4 4 8 8

>

> t(cbind(m1,m2)) [,1] [,2]

[1,] 1 1 [2,] 1 1 [3,] 2 2 [4,] 2 2

>

>

> diag(tulo) [1] 2 2 8 8

>

> diag(tulo)<-10

> tulo

[,1] [,2] [,3] [,4]

[1,] 10 2 4 4

[2,] 2 10 4 4 [3,] 4 4 10 8 [4,] 4 4 8 10

>

> diag(3)

[,1] [,2] [,3]

[1,] 1 0 0 [2,] 0 1 0 [3,] 0 0 1

>

> v<-c(10,20,30)

> diag(v)

[,1] [,2] [,3]

[1,] 10 0 0 [2,] 0 20 0 [3,] 0 0 30

>

> diag(3, nr=3, nc=5) [,1] [,2] [,3] [,4] [,5]

[1,] 3 0 0 0 0 [2,] 0 3 0 0 0 [3,] 0 0 3 0 0

>

>>

> a<-1:5

> b<-1:5

> ab<-a%o%b

> ab

[,1] [,2] [,3] [,4] [,5]

[1,] 1 2 3 4 5 [2,] 2 4 6 8 10 [3,] 3 6 9 12 15 [4,] 4 8 12 16 20 [5,] 5 10 15 20 25

> ab<-outer(a,b, "*")

>

> outer(a,b,"+")

[,1] [,2] [,3] [,4] [,5]

[1,] 2 3 4 5 6 [2,] 3 4 5 6 7 [3,] 4 5 6 7 8 [4,] 5 6 7 8 9

[5,] 6 7 8 9 10

>

> outer(a,b,"==")

[,1] [,2] [,3] [,4] [,5]

[1,] TRUE FALSE FALSE FALSE FALSE [2,] FALSE TRUE FALSE FALSE FALSE [3,] FALSE FALSE TRUE FALSE FALSE [4,] FALSE FALSE FALSE TRUE FALSE [5,] FALSE FALSE FALSE FALSE TRUE

>

> 1+abs(outer(1:5,1:5,"-") + )

[,1] [,2] [,3] [,4] [,5]

[1,] 1 2 3 4 5 [2,] 2 1 2 3 4 [3,] 3 2 1 2 3 [4,] 4 3 2 1 2 [5,] 5 4 3 2 1

> 0.5^abs(outer(1:5,1:5,"-")) [,1] [,2] [,3] [,4] [,5]

[1,] 1.0000 0.500 0.25 0.125 0.0625 [2,] 0.5000 1.000 0.50 0.250 0.1250 [3,] 0.2500 0.500 1.00 0.500 0.2500 [4,] 0.1250 0.250 0.50 1.000 0.5000

[5,] 0.0625 0.125 0.25 0.500 1.0000

>

> a<-matrix(c(2,8,2,-7,-9,-1,12,0,-16),nr=3,nc=3)

> a

[,1] [,2] [,3]

[1,] 2 -7 12 [2,] 8 -9 0 [3,] 2 -1 -16

> b<-c(4,7,-1)

> x<-solve(a,b)

> x

[1] 0.81967213 -0.04918033 0.16803279

> a %*% x [,1]

[1,] 4 [2,] 7 [3,] -1

>

> ai<-solve(a)

> ai %*% a

[,1] [,2] [,3]

[1,] 1.000000e+00 -2.220446e-16 -1.110223e-15 [2,] 5.551115e-17 1.000000e+00 -1.332268e-15 [3,] 6.938894e-18 3.122502e-17 1.000000e+00

>

> y<-c(1,1,2,2,3,3,3,2)

> x<-outer(1:8,0:2,"^")

> x

[,1] [,2] [,3]

[1,] 1 1 1 [2,] 1 2 4 [3,] 1 3 9 [4,] 1 4 16 [5,] 1 5 25 [6,] 1 6 36 [7,] 1 7 49 [8,] 1 8 64

> b<-solve(t(x) %*% x) %*% crossprod(x,y)

> b

[,1]

[1,] -0.33928571 [2,] 1.05357143 [3,] -0.08928571

> b<-lsfit(x,y)

Warning message:

X matrix was collinear in: lsfit(x, y)

> b

$coefficients

Intercept X1 X2 X3

-0.33928571 1.05357143 -0.08928571 0.00000000

$residuals

[1] 0.37500000 -0.41071429 -0.01785714 -0.44642857 0.30357143 0.23214286 0.33928571 -0.37500000

$intercept [1] TRUE

…

 eigen(t(x) %*% x)

$values

[1] 8968.5279284 15.0539754 0.4180962

$vectors

[,1] [,2] [,3]

[1,] 0.02310321 -0.4370079 0.89916089 [2,] 0.14633204 -0.8882360 -0.43545812 [3,] 0.98896571 0.1416365 0.04342716

>

> eigen(t(x) %*% x)$values

[1] 8968.5279284 15.0539754 0.4180962

>

> t<-eigen(t(x) %*% x)$vectors

> l<-diag(eigen(t(x) %*% x)$values)

>

> t(x) %*% x [,1] [,2] [,3]

[1,] 8 36 204 [2,] 36 204 1296 [3,] 204 1296 8772

>

> t %*% l %*% t(t) [,1] [,2] [,3]

[1,] 8 36 204 [2,] 36 204 1296 [3,] 204 1296 8772

>